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A New Extended Uniform Distribution

Received: 14 October 2016     Accepted: 7 November 2016     Published: 5 December 2016
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Abstract

We introduce a new family of distributions using truncated the Discrete Mittag- Leffler distribution. It can be considered as a generalization of the Marshall-Olkin family of distributions. Some properties of this new family are derived. As a particular case, a three parameter generalization of Uniform distribution is given special attention. The shape properties, moments, distributions of the order statistics, entropies are derived and estimation of the unknown parameters is discussed. An application in autoregressive time series modeling is also included.

Published in International Journal of Statistical Distributions and Applications (Volume 2, Issue 3)
DOI 10.11648/j.ijsd.20160203.12
Page(s) 35-41
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Discrete Mittag-Leffler Distribution, Entropy, Marshall-Olkin Family of Distributions, Maximum Likelihood, Random Variate Generation, Truncated Negative Binomial Distribution, Uniform Distribution

References
[1] H. Bidram, M. H. Alamastsaz and V. Nekoukhou, (2015). On an extension of the exponentiated Weibull distribution. Communications in Statistics - Simulation and Computation, 44, 1389-1404.
[2] G. M. Cordeiro and A. J. Lemonte, (2013). On the Marshall-Olkin extended Weibull distribution. Statistical Papers, 54, 333-353.
[3] K. Jayakumar and M. Thomas, (2008). On a generalization to Marshall-Olkin scheme and its application to Burr type XII distribution. Statistical Papers, 49, 421-439.
[4] K. K. Jose, S. R. Naik and M. M. Ristic, (2010). Marshall-Olkin q Weibull distribution and maximin processes. Statistical Papers, 51, 837-851.
[5] K. K. Jose and E. Krishna, (2011). Marshall-Olkin extended uniform distribution. ProbStat Forum, 04, 78-88.
[6] A. W. Marshall and I. Olkin, (1997). A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families. Biometrika, 84, 641-652.
[7] S. Nadarajah, K. Jayakumar and M. M. Ristic, (2013). A new family of life- time models. Journal of Statistical Computation and Simulation, 83, 1389-1404.
[8] R. N. Pillai and K. Jayakumar, (1995). Discrete Mittag-Leffler distributions. Statistics and Probability Letters, 23, 271-274.
[9] A. P. Prudnikov, Y. A. Brychkov and O.I Marichev, (1986). Integrals and series Vol. I, Gordeon and Breach Sciences, Amsterdam, Netherlands.
[10] M. M. Ristic and B. C. Popovic, (2000 a). A new Uniform AR(1) time series Model (NUAR(1)). Publications De Linstitut Mathematique Nouvelle series, 68, 145-152.
[11] M. M. Ristic and B. C. Popovic, (2000 b). Parameter estimation for Uniform autoregressive processes. Novi Sad Journal of Mathematics, 30, 89-95.
[12] M. M. Ristic, K. K. Jose and A. Joseph, (2007). A Marshall-Olkin gamma distribution and minification process. STARS International Journal (Science), 1, 107-117.
[13] M. M. Ristic and D. Kundu, (2015). Marshall-Olkin generalized exponential distribution. Metron, 73, 317-333.
Cite This Article
  • APA Style

    K. K. Sankaran, K. Jayakumar. (2016). A New Extended Uniform Distribution. International Journal of Statistical Distributions and Applications, 2(3), 35-41. https://doi.org/10.11648/j.ijsd.20160203.12

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    ACS Style

    K. K. Sankaran; K. Jayakumar. A New Extended Uniform Distribution. Int. J. Stat. Distrib. Appl. 2016, 2(3), 35-41. doi: 10.11648/j.ijsd.20160203.12

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    AMA Style

    K. K. Sankaran, K. Jayakumar. A New Extended Uniform Distribution. Int J Stat Distrib Appl. 2016;2(3):35-41. doi: 10.11648/j.ijsd.20160203.12

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  • @article{10.11648/j.ijsd.20160203.12,
      author = {K. K. Sankaran and K. Jayakumar},
      title = {A New Extended Uniform Distribution},
      journal = {International Journal of Statistical Distributions and Applications},
      volume = {2},
      number = {3},
      pages = {35-41},
      doi = {10.11648/j.ijsd.20160203.12},
      url = {https://doi.org/10.11648/j.ijsd.20160203.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijsd.20160203.12},
      abstract = {We introduce a new family of distributions using truncated the Discrete Mittag- Leffler distribution. It can be considered as a generalization of the Marshall-Olkin family of distributions. Some properties of this new family are derived. As a particular case, a three parameter generalization of Uniform distribution is given special attention. The shape properties, moments, distributions of the order statistics, entropies are derived and estimation of the unknown parameters is discussed. An application in autoregressive time series modeling is also included.},
     year = {2016}
    }
    

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    T2  - International Journal of Statistical Distributions and Applications
    JF  - International Journal of Statistical Distributions and Applications
    JO  - International Journal of Statistical Distributions and Applications
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    AB  - We introduce a new family of distributions using truncated the Discrete Mittag- Leffler distribution. It can be considered as a generalization of the Marshall-Olkin family of distributions. Some properties of this new family are derived. As a particular case, a three parameter generalization of Uniform distribution is given special attention. The shape properties, moments, distributions of the order statistics, entropies are derived and estimation of the unknown parameters is discussed. An application in autoregressive time series modeling is also included.
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Author Information
  • Department of Statistics, Sree Narayana College, Kerala, India

  • Department of Statistics, University of Calicut, Kerala, India

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